Strategy11Handout - Mixed Strategies Matching Pennies In...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
10/9/2008 1 Mixed Strategies – Matching Pennies ± In Matching Pennies, we found there was no Nash Equilibrium Guildenstern Heads Tails ± We expand the strategy set to allow for “mixed strategies” randomizations over Heads and Tales, the so-called “pure strategies” Rosencrantz Heads 1, -1 -1, 1 Tails -1, 1 1,-1 Why Mixed Strategies? ± If you were to play the same opponent repeatedly, you would like to be unpredictable . ± In rock-paper-scissors, if you behave predictably, your opponent will be able to beat you you. ± In a tennis match, you do not want your serves to be predicted by the opponent. Why Mixed Strategies? ± Maybe your opponent is picked from a large population of players… ± You play many times, each time with new opponent ± Each opponent does the same thing each time he plays ± Different opponents do different things ± You don’t know which type of opponent you get ± Model your opponent as randomly picking a strategy Why Mixed Strategies? ± Technical reason: Not all games have Nash equilibria in pure strategies. All games have Nash equilibria when allowing for mixed strategies. ± We are generalizing our notion of strategy ± pure strategies are a kind of mixed strategy ± where the probability distribution degenerates ± all the probability weight is on one pure strategy Mixed Strategies – Matching Pennies ± Rosencrantz’s strategy set is now a probability
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/14/2010 for the course ECON 398 taught by Professor Emre during the Spring '07 term at University of Michigan.

Page1 / 4

Strategy11Handout - Mixed Strategies Matching Pennies In...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online